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Let's imagine I have a perfectly known signal $s(t)$ and I want to analyze its frequency components.

I noticed that mostly everyone would use the PSD of $s(t)$ to do that, instead of simply use the magnitude of the Fourier transform of $s(t)$. Is there a reason for that ?

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    $\begingroup$ You can't "use" the PSD to analyze the frequency components. It is exactly that which you analyze. The Fourier transform is in fact an important way / step in estimating the PSD – so I'm not sure what you're asking here... $\endgroup$
    – Marcus Müller
    Jun 18, 2020 at 8:34

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The power spectral density (PSD) is a natural measure of the signal's power content with respect to frequency. A central part of non-parametric signal processing is to provide a "best" estimate of the "true" PSD from knowing only one or some "realizations" with finite length. By taking into account the influence of stationary random processes, it should be noted that the Fourier transform is not defined for processes with infinite energy.

However, by looking at the second-order properties (autocorrelation), the true PSD can be well-defined, and the Fourier transform of the realization (on a finite horizon) can be used to provide an estimate of it.

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    $\begingroup$ This reminded me of something mentioned in The Measurement of Power Spectra by Blackman and Tukey: "While the modified apparent autocovariance functions...are often far from being respectable estimates of the true autocovariance function, their transforms are very respectable estimates of smoothed values of the true spectral density." (page 12 in the 1955 Dover edition) $\endgroup$
    – Joe Mack
    Jun 18, 2020 at 16:25

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